The lower quartile, median and upper quartile are usually denoted by Q_1, Q_2 and Q_3. To find them you must first arrange the data in order of size.
If n is odd, then Q_2 is the \frac{1}{2}(n+1)th value. If n is even the median is halfway between the \frac{1}{2}nth value and the next.
To find Q_1 find the median of the lower half of the data. To find Q_3, find the median of the upper half of the data.
If n is odd, then Q_2 is the \frac{1}{2}(n+1)th value. If n is even the median is halfway between the \frac{1}{2}nth value and the next.
To find Q_1 find the median of the lower half of the data. To find Q_3, find the median of the upper half of the data.
Software/Applets used on this page
Glossary
median
the middle value of a set of data that has been arranged in order of magnitude; half the data values are above it and half are below.
quartile
In an ordered set of data 25% are below the first (Q1), 50% are below the second (Q2), 75% are below the third (Q3).
union
The union of two sets A and B is the set containing all the elements of A and B.
This question appears in the following syllabi:
| Syllabus | Module | Section | Topic | Exam Year |
|---|---|---|---|---|
| AQA A-Level (UK - Pre-2017) | S1 | Summarising data | Measures of location | - |
| AQA AS Maths 2017 | Statistics | Data Presentation and Interpretation | Measures of Central Tendency | - |
| AQA AS/A2 Maths 2017 | Statistics | Data Presentation and Interpretation | Measures of Central Tendency | - |
| CBSE XI (India) | Statistics and Probability | Statistics | Range, mean deviation, variance and standard deviation of grouped data | - |
| CCEA A-Level (NI) | S1 | Summarising data | Measures of location | - |
| CIE A-Level (UK) | S1 | Summarising data | Measures of location | - |
| Edexcel A-Level (UK - Pre-2017) | S1 | Summarising data | Measures of location | - |
| Edexcel AS Maths 2017 | Statistics | Measures of Data | Measures of Central Tendency | - |
| Edexcel AS/A2 Maths 2017 | Statistics | Measures of Data | Measures of Central Tendency | - |
| I.B. Standard Level | 5 | Summarising data | Measures of location | - |
| Methods (UK) | M14 | Summarising data | Measures of location | - |
| I.B. (MSSL) | 6 | Summarising data | Measures of location | - |
| OCR A-Level (UK - Pre-2017) | S1 | Summarising data | Measures of location | - |
| OCR AS Maths 2017 | Statistics | Central Tendency and Variation | Measures of Central Tendency | - |
| OCR MEI AS Maths 2017 | Statistics | Central Tendency and Variation | Measures of Central Tendency | - |
| OCR-MEI A-Level (UK - Pre-2017) | S1 | Summarising data | Measures of location | - |
| Pre-U A-Level (UK) | Prob | Summarising data | Measures of location | - |
| Scottish (Highers + Advanced) | HS | Summarising data | Measures of location | - |
| Scottish Highers | S | Summarising data | Measures of location | - |
| Universal (all site questions) | S | Summarising data | Measures of location | - |
| WJEC A-Level (Wales) | S1 | Summarising data | Measures of location | - |